Parameter estimation for Fisher–Snedecor diffusion

We consider the problem of parameter estimation for an ergodic diffusion with Fisher–Snedecor invariant distribution, to be called Fisher–Snedecor diffusion. We propose moments-based estimators of unknown parameters, based on both discrete and continuous observations, and prove their consistency and asymptotic normality. The explicit form of the asymptotic covariance matrix is determined by using the properties of eigenfunctions (Fisher–Snedecor polynomials) of the corresponding Sturm–Liouville operator